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The Didactical Challenge of Symbolic Calculators


The Didactical Challenge of Symbolic Calculators

Turning a Computational Device into a Mathematical Instrument
Mathematics Education Library, Band 36

von: Dominique Guin, Kenneth Ruthven, Luc Trouche

178,49 €

Verlag: Springer
Format: PDF
Veröffentl.: 30.03.2006
ISBN/EAN: 9780387234359
Sprache: englisch
Anzahl Seiten: 305

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Beschreibungen

A significant driver of recent growth in the use of mathematics in the professions has been the support brought by new technologies. Not only has this facilitated the application of established methods of mathematical and statistical analysis but it has stimulated the development of innovative approaches. These changes have produced a marked evolution in the professional practice of mathematics, an evolution which has not yet provoked a corresponding adaptation in mathematical education, particularly at school level. In particular, although calculators -- first arithmetic and scientific, then graphic, now symbolic -- have been found well suited in many respects to the working conditions of pupils and teachers, and have even achieved a degree of official recognition, the integration of new technologies into the mathematical practice of schools remains marginal. It is this situation which has motivated the research and development work to be reported in this volume. The appearance of ever more powerful and portable computational tools has certainly given rise to continuing research and development activity at all levels of mathematical education. Amongst pioneers, such innovation has often been seen as an opportunity to renew the teaching and learning of mathematics. Equally, however, the institutionalization of computational tools within educational practice has proceeded at a strikingly slow pace over many years.
A significant driver of recent growth in the use of mathematics in the professions has been the support brought by new technologies. Not only has this facilitated the application of established methods of mathematical and statistical analysis but it has stimulated the development of innovative approaches. These changes have produced a marked evolution in the professional practice of mathematics, an evolution which has not yet provoked a corresponding adaptation in mathematical education, particularly at school level. In particular, although calculators -- first arithmetic and scientific, then graphic, now symbolic -- have been found well suited in many respects to the working conditions of pupils and teachers, and have even achieved a degree of official recognition, the integration of new technologies into the mathematical practice of schools remains marginal. It is this situation which has motivated the research and development work to be reported in this volume. The appearance of ever more powerful and portable computational tools has certainly given rise to continuing research and development activity at all levels of mathematical education. Amongst pioneers, such innovation has often been seen as an opportunity to renew the teaching and learning of mathematics. Equally, however, the institutionalization of computational tools within educational practice has proceeded at a strikingly slow pace over many years.
Acknowledgments.- Introduction, Dominique Guin, Kenneth Ruthven and Luc Trouche.- Calculators in mathematics education: a rapid evolution of tools, with differential effects, Luc Trouche.- A CAS as an assistant to reasoned instrumentation, Philippe Elbaz-Vincent.- Transposing computer tools from the mathematical sciences into teaching, Jean-Baptiste Lagrange.- The influence of a computer algebra environment on teachers’ practice, Margaret Kendal, Kaye Stacey and Robyn Pierce.- Using symbolic calculators to study mathematics, Jean-Baptiste Lagrange.- An instrumental approach to mathematics learning in symbolic calculators environments, Luc Trouche.- Computer algebra as an instrument: examples of algebraic schemes, Paul Drijvers and Koeno Gravemeijer.- Instrumental genesis, individual and social aspects, Luc Trouche.- The integration of symbolic calculators into secondary education: some lessons from didactical engineering, Michèle Artigue.- Conclusion, Dominique Guin, Kenneth Ruthven and Luc Trouche.-Index.
While computational technologies are transforming the professional practice of mathematics, as yet they have had little impact on school mathematics. This pioneering text develops a theorized analysis of why this is and what can be done to address it. It examines the particular case of symbolic calculators (equipped with computer algebra systems) in secondary education. Drawing on a substantial program of French innovation and research, as well as closely related studies from Australia and the Netherlands, it provides rich illustrations of the many aspects of technology integration, and of the ways in which these are shaped at different levels of the educational institution.

This text offers the first English-language exposition of how an innovative synthesis of the theories of instrumentation and didactics can be used to illuminate the complexities of technology integration. It offers important guidance for policy and practice through its analysis of the central role of the teacher and its identification of key principles for effective didactical design and management. These distinctive features make this book essential reading for researchers, teacher educators, and graduate students in mathematics education and technology in education, as well as for teachers of mathematics at upper-secondary and university levels.

This is a revised, English-language edition of D. Guin & L. Trouche (Eds.) (2002) Calculatrices symboliques. Transformer un outil en un instrument de travail mathématique: un problème didactique (Editions La Pensée Sauvage, Grenoble).
Offers the first English-language exposition of how an innovation synthesis of the theories of instrumentation and didactique can be used to illuminate the complexities of technology integration